Details

sample42.0ms

Algorithm

intervals

Results

18.0ms	282×	body	80	valid
4.0ms	91×	body	80	nan

simplify4.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
3.8b	(* (* x y) z)
7.9b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
22.9b	(sqrt (- (* z z) (* t a)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
11×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
9×	`sqrt-prod`
6×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod` `add-log-exp`
4×	`sqrt-div`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-r` `pow-prod-down` `flip--`
2×	`associate-/r/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-l` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 76

Calls

4 calls:

8.0ms	(- (* z z) (* t a))
18.0ms	(* (* x y) z)
45.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
9.0ms	(sqrt (- (* z z) (* t a)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (* z z) (* t a))
31.0ms	(* (* x y) z)
115.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
86.0ms	(sqrt (- (* z z) (* t a)))

simplify42.0ms

Counts: 88 → 88

prune352.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
0.4b	(- (* z z) (* t a))
4.1b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
22.9b	(sqrt (- (* z z) (* t a)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
47×	`add-sqr-sqrt`
46×	`add-cube-cbrt` `*-un-lft-identity`
33×	`sqrt-prod`
25×	`associate-/r*`
18×	`add-exp-log` `add-cbrt-cube`
7×	`cbrt-undiv` `div-exp` `associate-/l*`
6×	`add-log-exp`
5×	`pow1`
4×	`sqrt-div` `div-inv`
3×	`flip3--` `flip--`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/r/`

Counts

4 → 132

Calls

4 calls:

18.0ms	(/ (sqrt (- (* z z) (* t a))) z)
9.0ms	(- (* z z) (* t a))
44.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
10.0ms	(sqrt (- (* z z) (* t a)))

series409.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ (sqrt (- (* z z) (* t a))) z)
61.0ms	(- (* z z) (* t a))
133.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
96.0ms	(sqrt (- (* z z) (* t a)))

simplify60.0ms

Counts: 144 → 144

prune936.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
1.3b	(/ y (/ (sqrt (- (* z z) (* t a))) z))
2.2b	(* (/ x (sqrt 1)) (/ y (/ (sqrt (- (* z z) (* t a))) z)))
22.9b	(sqrt (- (* z z) (* t a)))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

308×	`times-frac`
216×	`add-sqr-sqrt`
159×	`*-un-lft-identity`
155×	`add-cube-cbrt`
87×	`sqrt-prod`
71×	`associate-r`
30×	`add-exp-log` `add-cbrt-cube`
22×	`associate-l` `associate-/r*`
16×	`unswap-sqr`
12×	`cbrt-undiv` `div-exp`
10×	`div-inv`
7×	`pow1`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`associate-/l*`
2×	`flip3--` `sqrt-div` `associate-/r/` `flip--`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 266

Calls

4 calls:

17.0ms	(- (* z z) (* t a))
33.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
109.0ms	(* (/ x (sqrt 1)) (/ y (/ (sqrt (- (* z z) (* t a))) z)))
18.0ms	(sqrt (- (* z z) (* t a)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* z z) (* t a))
88.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
111.0ms	(* (/ x (sqrt 1)) (/ y (/ (sqrt (- (* z z) (* t a))) z)))
71.0ms	(sqrt (- (* z z) (* t a)))

simplify54.0ms

Counts: 278 → 278

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.4b

localize38.0ms

Local error

Found 4 expressions with local error:

4.5b	(cbrt (/ (sqrt (- (* z z) (* t a))) z))
22.9b	(sqrt (- (* z z) (* t a)))
22.9b	(sqrt (- (* z z) (* t a)))
22.9b	(sqrt (- (* z z) (* t a)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`cbrt-prod`
20×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
7×	`pow1`
6×	`sqrt-div`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 76

Calls

4 calls:

11.0ms	(cbrt (/ (sqrt (- (* z z) (* t a))) z))
16.0ms	(sqrt (- (* z z) (* t a)))
16.0ms	(sqrt (- (* z z) (* t a)))
21.0ms	(sqrt (- (* z z) (* t a)))

series513.0ms

Counts

4 → 12

Calls

4 calls:

226.0ms	(cbrt (/ (sqrt (- (* z z) (* t a))) z))
82.0ms	(sqrt (- (* z z) (* t a)))
105.0ms	(sqrt (- (* z z) (* t a)))
100.0ms	(sqrt (- (* z z) (* t a)))

simplify147.0ms

Counts: 88 → 88

prune589.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 3.4b

regimes561.0ms

Accuracy

85.7% (2.8b remaining)

Error of 6.0b against oracle of 3.1b and baseline of 23.0b

bsearch100.0ms

Steps

Iters	Range		Point
9	6.663579023451854e+147	9.351805393147033e+156	1.9720317117511606e+149
7	-7.495622944610967e+154	-1.314778648009767e+153	-1.6391293784153955e+153

simplify25.0ms

end0.0ms

sample1.7s

Algorithm

intervals

Results

669.0ms	8845×	body	80	valid
161.0ms	3033×	body	80	nan